56.3.20 problem 20

Internal problem ID [8878]
Book : Own collection of miscellaneous problems
Section : section 3.0
Problem number : 20
Date solved : Sunday, March 30, 2025 at 01:45:30 PM
CAS classification : [[_high_order, _with_linear_symmetries]]

\begin{align*} 5 x^{5} y^{\prime \prime \prime \prime }+4 x^{4} y^{\prime \prime \prime }+x^{2} y^{\prime }+x y&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 38

ode:=5*x^5*diff(diff(diff(diff(y(x),x),x),x),x)+4*x^4*diff(diff(diff(y(x),x),x),x)+x^2*diff(y(x),x)+x*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \moverset {4}{\munderset {\textit {\_a} =1}{\sum }}x^{\operatorname {RootOf}\left (5 \textit {\_Z}^{4}-26 \textit {\_Z}^{3}+43 \textit {\_Z}^{2}-21 \textit {\_Z} +1, \operatorname {index} =\textit {\_a} \right )} \textit {\_C}_{\textit {\_a}} \]

✓ Mathematica. Time used: 1.457 (sec). Leaf size: 1931

ode=5*x^5*D[y[x],{x,4}]+4*x^4*D[y[x],{x,3}]+x^2*D[y[x],x]+x*y[x]== Sin[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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✓ Sympy. Time used: 0.344 (sec). Leaf size: 97

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(5*x**5*Derivative(y(x), (x, 4)) + 4*x**4*Derivative(y(x), (x, 3)) + x**2*Derivative(y(x), x) + x*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} x^{\operatorname {CRootOf} {\left (5 x^{4} - 26 x^{3} + 43 x^{2} - 21 x + 1, 0\right )}} + C_{2} x^{\operatorname {CRootOf} {\left (5 x^{4} - 26 x^{3} + 43 x^{2} - 21 x + 1, 1\right )}} + C_{3} x^{\operatorname {CRootOf} {\left (5 x^{4} - 26 x^{3} + 43 x^{2} - 21 x + 1, 2\right )}} + C_{4} x^{\operatorname {CRootOf} {\left (5 x^{4} - 26 x^{3} + 43 x^{2} - 21 x + 1, 3\right )}} \]